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THE HAYSTACK-MILLSTONE INTERFEROMETER SYSTEM
ALAN E. E. ROGERS
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7
TECHNICAL REPORT 457
MARCH 15, 1967
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
RESEARCH LABORATORY OF ELECTRONICS
CAMBRIDGE, MASSACHUSETTS
The Research Laboratory of Electronics is an interdepartmental
laboratory in which faculty members and graduate students from
numerous academic departments conduct research.
The research reported in this document was made possible in
part by support extended the Massachusetts Institute of Technology, Research Laboratory of Electronics, by the JOINT SERVICES ELECTRONICS PROGRAMS (U.S. Army, U.S. Navy, and
U.S. Air Force) under Contract No. DA 36-039-AMC-03200(E);
additional support was received from the National Aeronautics and
Space Administration (Grant NsG-419).
Reproduction in whole or in part is permitted for any purpose
of the United States Government.
Qualified requesters may obtain copies of this report from DDC.
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
RESEARCH LABORATORY OF ELECTRONICS
March 15, 1967
Technical Report 457
THE HAYSTACK-MILLSTONE
INTERFEROMETER SYSTEM
Alan E. E. Rogers
(Manuscript received January 13, 1967)
Abstract
The Haystack 120-ft antenna and the Millstone 84-ft antenna have been coupled
together to form a radiometric interferometer. At 18-cm wavelength, which was chosen
for a study of galactic OH emission, the interferometer has a minimum fringe spacing
of 54 seconds of arc. The interferometer synthesizes a beam approximately equivalent
to that of a 2000-ft parabolic antenna and can measure positions to a small fraction of
the fringe spacing. The interferometer uses a digital correlator to analyze the fringe
amplitude and phase as a function of frequency. This enables mapping of spectral features. The design and construction are described, as well as the theory and method of
data reduction. A noise analysis shows that the threshold level could be reduced by
It is shown that for radiometric studies
using more complex processing techniques.
many of the capabilities of a very large antenna can be synthesized, with smaller
antennas and complex data-processing equipment taking the place of mechanical structure.
-i
a)
0
I
o
c)
tl'
1
TABLE OF CONTENTS
I.
INTRODUCTION
1
II.
DESIGN AND CONSTRUCTION
2
2.1
2
III.
Radio-Frequency Part of the System
2. 2 Intersite Coupling
2
2. 3 Digital Correlation and Data-Recording System
5
2.4 Construction
5
2. 5 System Tests
5
THEORY OF OPERATION AND METHOD OF DATA REDUCTION
9
3.1 Geometry
9
3. 2 Computation of Spectral Fringe Amplitude and Phase
10
3. 3 Fringe Amplitude and Phase for Continuum Sources
13
3. 4 Normalized Autocorrelation Functions and Power Spectra from
the Digital Correlator
14
3. 5 System Calibration
15
3. 6 Distribution of Brightness Temperature and Source Positions
from Fringe Amplitude and Phase
17
3. 7 Computer Programs
19
IV.
INTERFEROMETER NOISE ANALYSIS
22
V.
POLARIZATION ANALYSIS
29
VI.
CONCLUSION
31
APPENDIX
Fortran Statement of the Program
32
Acknowledgment
40
References
41
v
I.
INTRODUCTION
The 120-ft antenna of the Haystack Microwave Research Facility and the 84-ft antenna
of the Millstone Radar Facility used as an interferometer makes a powerful instrument
for high resolution radiometric studies.
2250 ft along a line approximately 19
°
The antennas are separated by approximately
East of North.
This baseline gives a minimum
fringe spacing of 54 seconds of arc at 18 cm and provides a good range of projected baseline for a wide range of declination. The convenient baseline, and the spectral processing
equipment at Haystack make the system ideal for a study of OH emission regions that
were unresolved with a single antenna.
This report describes the design and theory of the interferometer.
1
II.
DESIGN AND CONSTRUCTION
2. 1 RADIO-FREQUENCY PART OF THE SYSTEM
A block diagram of the Millstone receiver front end is shown in Fig. 1. Circular and
linear polarization is obtained from a dual-mode horn whose output ports give vertical
and horizontal polarization. Combination of vertical and horizontal signals through a
hybrid complex give left- and right-circular polarization after correct adjustment of the
phase lengths. The antenna output is amplified by a tunnel diode amplifier and then filtered to reject the image band.
A ferrite switch is included for calibration measure-
ments.
In the normal interferometer mode the switch remains switched to the antenna
A noise source is used for single antenna measurements and system temperature
measurement.
side.
The local-oscillator signal is derived by phase-locking an oscillator to the sum or
difference of a harmonic of 67 MHz and a signal whose frequency could be varied approxFor the OH emission measurements the 24 t h harmonic was selected.
The output of the oscillator was filtered to attenuate any spurious signals that tend to
be produced by the synchronizer.
A block diagram of the local-oscillator system is
imately 28 MHz.
shown in Fig. 2.
The mixer output is amplified by a 30-MHz amplifier with a 10-MHz bandwidth. A
line driver then boosts the level to 100 Mw. The Haystack receiver front end did not
require the line driver, owing to its proximity to the control room where the IF outputs
are combined.
Otherwise the Haystack front end is similar to that at Millstone.
2.2 INTERSITE COUPLING
The intersite coupling of the radiometers involves the transmission of antennapointing commands to Millstone, remote control of the radiometer, transmission of the
intermediate frequency to Haystack, and two-way coupling of the local-oscillator reference signals. To maintain good phase stability, the reference signals are transmitted
along a servo-controlled line that nullifies line-length changes caused by temperature
change and other effects. The transmission system also has to overcome a large line
attenuation of 55 db for one-way transmission at 67 MHz. The selection of a lower basic
frequency would have reduced attenuation but would have made phase-locking to L-band
more difficult.
A block diagram of the line servo is shown in Fig. 3.
The 67-MHz
reference signal is amplified to approximately 1 watt and transmitted to the line
through a hybrid junction. At the receiving end of the line a portion of the signal
is reflected.
The reflected signal undergoes phase reversal with a 100-kHz rate
as the diode switch modulates the reflection coefficient from +
to
-
-.
Very little
of the 100-kHz modulation is passed into the 67-MHz amplifier, because of the isolation afforded by the hybrid tee. At the transmitting end, the reflected signal is
2
FERRITE
DUAL
HORN
IF OUTPUT
TO LINE
I OOmW
Fig. 1.
Radio-frequency section of the Millstone Receiver.
MHz
08 MHz
Fig. 2.
Local-oscillator system shown for the center of the band at 1666 MHz.
3
___ ..____1_11111_1_1_·1__11__111111_11__11_-
·1.
·_-
28MHz
OdBm
MOTOR-DRIVEN
67MH
I
AMPLIFIER
I
POWER
I
67MH
r
LIESTRETCER
MIXER
FAIER
OUT
REFLECTED
SIGNAL
-10
OdBm
HEOUTIZER
INTERSITE
PHASE
PDETECTOR
ATAC
WITC
"HIN
K
REFERENCE
SWIRN
CHNMPOTERE
GIN
APE
+WNI
I
T
ELEOA;I1
SERVO
AZM
R
00 MRz
SER O JLNE
RIT
I
5.
Fig.
Halso
EVs
I
E
LEF
67MWz
28MW
POWER
II
|
TRANMISO
Mz||28MWz
±067
I
TRANSMISSION
REF
I
R
I
SYNTHESIZERT
RIG
30M
I
AZMO
SERVO
ITI
SWITCHING
11PE
5
.
4
H
y
ELEV
AT ONE
SERVOE
I I
--
Fig.
itrermtr
TA
300
t
1ERENCE
TaJ,,~
~~jcco
kM2tn
COPER
l
mixed with the 67-MHz reference signal and amplified.
fier is proportional to cos
cos 27ft,
The output of the 100-kHz ampli-
where f = 100 kHz, and
67-MHz signal after having traveled twice the line length.
is the phase of the
Multiplication of this sig-
nal by the 100-kHz reference signal produces the necessary error signal from the
servo loop.
The high loop gain makes it possible for the line servo to maintain a con-
stant electrical line length to within a small fraction of an inch.
2.3 DIGITAL-CORRELATION AND DATA-RECORDING SYSTEM
The IF signals are either added or subtracted as shown in Fig. 4.
signal is filtered and converted to video.
The combined
The autocorrelation function of the clipped
and sampled video signal is taken with a digital correlator.
Autocorrelation functions
of the sum and difference signals are transferred alternately to a computer every
100 msec.
The basic correlation period is 87. 5 msec.
The system is blanked for
12. 5 msec while the data are being transferred to the U490 computer.
Signal bandwidths
of 4 MHz, 1. 2 MHz, 400 kHz, 120 kHz, and 40 kHz, can be analyzed by selecting appropriate filter and sampling frequencies.
word for each of 100 delays.
switching reference signal.
An extra bit is
used to indicate the state of the
The autocorrelation functions, together with continuum
data, bandwidth and correlator mode,
are transferred to magnetic tape.
in Fig.
The autocorrelation function is a 16-bit binary
and antenna command azimuth and elevation
A block diagram of the whole system is shown
5.
2.4 CONSTRUCTION
Figure 6 shows various sections of the interferometer equipment.
front end is located at the primary focus of the antenna,
The Millstone
and the output of the tunnel
diode amplifier is fed via a heliax cable to the equipment box on the azimuth deck.
The mixer and the local-oscillator system are located in the equipment box,
which
is connected by the intersite cables to the radiometer box at the Haystack secondary
focus.
The phase combiner and digital correlator are located in the Haystack con-
trol room from which both radiometers can be controlled by remote switching.
2.5 SYSTEM TESTS
Single-antenna measurements were made to measure the aperture efficiencies.
The antenna temperatures of Cassiopeia A were 160°K and 180°K, which indicated
efficiencies of 40% and 25% for the Millstone and Haystack antennas,
respectively.
The very low efficiency for Haystack is attributed to feed losses and the flow of
energy past the Cassegranian subreflector which is in the near field of the feed
horn at 18 cm.
The efficiency of Millstone is close to what one would expect after
5
1_1_·____1________1__________141111__
-
---· ·-
-
-(-- -
(a )
Fig. 6.
JD)
(a) Control panel for the Millstone receiver.
(b) Haystack receiver rack.
6
__
__
______
..
rd
(c)
Fig. 6.
(d)
(c) Motor-driven line stretcher.
(d) Lowering of Millstone subreflector to make way for a prime-focus feed.
7
_
_
_I
_
_
_I
_
_
I
_11
-.1·11-111-
...Il_--il_-rl--Y11P-l----
-1_^11_^-·---·1_11O
111
11
)----·II
-
------- ·----·
-
estimating the aperture blockage produced by the subreflector.
For operation in the
radiometric mode the Millstone subreflector was lowered to the vertex, as shown in
Fig. 6d, to allow an L-band horn to be used at the primary focus.
After checking the individual radiometers
for linearity,
bandpass,
and lack of
spurious signals, the system was checked for phase coherence and phase stability. The
test arrangement is illustrated in Fig. 7. A signal from a test oscillator is connected
to each radiometer individually and then simultaneously.
When the oscillator is swept
in frequency the bandpass is displayed when only one radiometer is connected to the
When both radiometers are swept simultaneously fringes appear, because
of the phase relationship between the radiometer outputs. The fringe spacing in Hz is
oscillator.
the reciprocal of the delay in seconds.
Measurement of the fringe pattern and bandpass
functions showed that the phase noise in the system produced less than 2% reduction in
fringe amplitudes. The phase stability was better than 50' during 24 hours. Some of
this shift may have been due to the measuring technique, as observations of continuum
radio sources indicated better stability.
SWEEP
ATO
OSCIL
- 3000 X
AIR PATH
-20 dBm
+
MILLSTONE
RECE IVER
VARIABLE I
ATTENUATOR
RECEIVER
tBANDWIDTH
400kHz
FILTER
BANDPASS
SQUARE
LAW
DETECTOR
CORRELATOR
OSCILLOSCOPE
FRINGES/
Fig. 7.
Test arrangement for measuring phase coherence.
The trombone section of the line servo in Fig. 6c was observed to move approximately 5 ft during the sunrise and sunset period when the temperature changed about
50 0 F.
Finally, observations of unpolarized continuum radio sources with the interferometer
confirmed the isolation between the two circular modes of the feeds to be better than
20 db.
8
III.
THEORY OF OPERATION AND METHOD OF DATA REDUCTION
3. 1 GEOMETRY
The interferometer geometry is shown in Fig. 8.
are centered at Haystack.
Azimuth and elevation coordinates
r 1 is a fixed vector from the intersection of the azimuth axis
and a horizontal plane through the elevation axis at Millstone to the intersection of the
azimuth and elevation axes of Haystack.
r 2 is the vector from the origin of r
to the
intersection of a line to the source through the vertex intersecting the elevation axis of
Millstone; therefore, r 2 is the offset of the elevation axis of Millstone from its azimuth
axis.
A
r 3 is a unit vector toward the apparent position of the source.
If the source position is unknown, then r3 is in the direction of a reference position in the sky relative to
which the source distribution is to be mapped.
r1 = D sin EH iz
+
D cos EH sin AH
r 2 = d sin AS ix + d cos AS iy
ix +
These vectors may be expressed as
D cos EH cos AH iy
(1)
(Differences in zenith neglected)
(2)
(3)
r 3 = sin E S iz + cos E S sin A S ix + cos E S cos A S iy.
where D is the distance between Haystack and Millstone, d is the offset of the elevation
axis from the azimuth axis for the Millstone antenna,
AS and E S are the apparent
iz (ZENITH)
iy(
-
INTERSECTIONC
AZIMUTH AND E
AXES AT HAYSTA
(EAST)
Fig. 8.
INTERSECTIO
AZIMUTH AX
HORIZONTA
THROUGH EL
AXIS AT MIL
Interferometer geometry.
- ELEVATION AXIS
OF MILLSTONE
azimuth and elevation of the source as seen from Haystack, and AH and EH are the azimuth and elevation of Haystack from Millstone in the Haystack coordinate system.
The portion of the interferometer delay which is azimuth- and elevation-dependent
is given by
Tt
=
(l-r2)
D
=D
sin E
'r3
sin E S
S + D
os E
cos E
cos (AA
d
cos E
dcos
E
(4)
9
_
I I I_ 1
110111111111*1- -^11__1_._1--·-)11Ill(illli·LI-l·
1
IlI II
-
-II
Since A S and E S is a function
of time,
so is
Tt.
3. 2 COMPUTATION OF SPECTRAL FRINGE AMPLITUDE AND PHASE
The signal from a point source is a plane wave that arrives at one antenna before
The spectrum of the delayed signal is the same, but the frequency components
the other.
in the Fourier analysis of the signal are phase-shifted.
power spectrum of the added signal is modulated.
If the signals are added, the
This can be seen in the following way:
If we let x(t) be the received signal voltage,
x()
=
x(t) e
dt,
(5)
o0
then the Fourier transform of the delayed signal is
+00
x(o) ='
-ia)T
1
.
X(t-ri) elt
dt = e
x(@).
(6)
The power spectra of the sum and difference of the signals with and without delay are
S+(o) = Ix(o) 12 (2+2 cos WTi )
(7)
2 (2-2 cos coTi),
(8)
and
S_()
= x()
where S+(w) and S_()
tively.
are the power spectra of the added and subtracted signals, respec-
The phase that results from the interferometer delay Ti can be expressed as the
sum of component phases, according to the following equation.
CT i = (o+h))(Tt+Tj+T')
= oTt +
OTa + AC(T t+T ) +
(9)
OT',
where the delay is decomposed into Tt (as given in Eq. 4), the geometric delay for a
reference position in the sky, T, the delay in the cables and amplifiers, and T', the delay
resulting from an offset of the point source from the reference point.
The reference
position is chosen to be the position toward which the main beams of the individual
antennas are directed or the center of the region being mapped. coTt is called the reference phase, cooTI the instrumental phase, and A(Tt+TI) is a frequency-dependent phase.
OT' is the phase developed, because of an offset of the point source from the reference
phase. It is called the "fringe phase," since, in a complex source distribution, it is the
phase of the Fourier component of the source distribution for the interferometer projected baseline at time t.
offset.
-2° is the center of the observed band, and -y
is the frequency
cwTt produces a fringe pattern in the sky, and is a function of time owing to the
earth's motion.
10
Acrai produces fringes
across the spectrum
ence of the fringe pattern on frequency.
or equivalently expresses the depend-
When A
i
is
small and there is
only
a fraction of a fringe over the analyzed spectrum, the interferometer is said to be in
the "white fringe region," In a spectral interferometer it is only necessary to maintain
the white-fringe condition over the resolution bandwidth, not the total bandwidth that is
analyzed.
Thus far, only a point source has been considered.
If it is assumed that different
points in the sky radiate independently, then the receiver power spectrum will be just
the summation of power spectra from the individual points and the difference power
spectra becomes
SD(a) = S+(a)) - S_()
=
Xk()
E
2 4 cos
(T
(10)
i.
k
The only portion of xi which changes with the summation variable, k, is aTk.
Using
complex quantities, we have
SD()
=
12 4Re
ixk()
e
1
k
4 Re e
xk(c)
2
eiT
k
e
=Re A()
where A(X) ;and caT'()
i
()
( 1)
e
are known as the fringe amplitude and phase.
In summing over
the elementary points that make up the source distribution, the resultant phase CT'(C)
is a frequency-dependent quantity.
The relation of these quantities to the brightness
temperature distribution is discussed in section 3. 6.
During one integration period, typically of 10 or 15 minutes, all of the phases except
the reference phase
wT o
remain constant to a few degrees for a source distribution con-
tained within a few minutes of arc from the reference position.
Limits for the rate of
change of fringe and reference phases for the Haystack-Millstone baseline are given by
dw ot Tt < 1 radian sec -1
dt
dwoT l
dt
dt
dt.
dt
0
(Phase-stable system)
<
-radians
< 3 X 10
4
radians
sec
(minutes of arc displacement)
11
1 sec1
The average fringe amplitude and phase over the integration period are determined by
making a least-squares fit of the spectral difference to a function given in Eq. 11.
That is,
we wish to minimize
(SD, t(o)-a(o) cos (OoTt-b(w) sin
o
t)12)
t
where
a(X) = A(w) cos (o rTI+A(To+
)+oT '())
(13)
b(w)
)+WTtI())
(14)
=
-A(w)
sin (oo0 T+AO(To+T
(t+T)
Tt +
2
To
(15)
T = Integration period.
(16)
At
At
SD t(w) is the power spectrum difference for a time interval from t- 2 to t + 2t
When the digital correlator is used, At = 200 msec.
The reference phase change
o(
t-
Tt)
must be small for this fringe-filtering scheme to work satisfactorily;
otherwise the fringes are smeared in the difference spectrum.
The addition of a fre-
quency offset in one of the local oscillators can obviate this problem, but this was unnecessary for the Haystack-Millstone interferometer.
Minimizing the expression above, we obtain
'()
=RX(w) - PY(w))
QX(w) - RY()
-
with quadrant identification
)
- X
l
(17)
and
y(w)(R 2+P2)+
X()(Q2+R2
-2Y(w) X(w) R(P+Q)
22
r
(PQ-R)
J
A(X)
(18)
where
X(a)) =
SD, t()
cos
o'rt
(19)
SD,t()
sin wort
(20)
t
Y(o) =
E
t
12
P =
cos
Tt
(21)
CoTt
(22)
sin wo0T cos wo
0 t.
(23)
c
t
Q=
sin
t
R =
t
The sine-cosine multiplications can be performed on the autocorrelation functions
before taking a Fourier transform by interchanging the order of summation. In practice,
this is done to save computation time.
3.3 FRINGE AMPLITUDE AND PHASE FOR CONTINUUM SOURCES
For a continuum source T' is not a function of c and neither is the fringe amplitude A
a function of o, provided the source spectrum is flat.
Since determining spectral fringe
phase and amplitude for a continuum source gives no additional information, and we
would like to reduce the noise in the measurement by averaging over the bandwidth, it
is desirable to modify the fringe filtering process.
To do this, the least-squares fit is
determined by summation over frequency in addition to time.
E
c
(SD, t(c)-a cos ooTt-b sin
oTt) 2 = minimum.
(24)
t
Here we have used the following definitions:
a = A cos ( oTI+A(T+T
(25)
)+T')
(26)
b = -A sin (OTI+AC(T+Tj)+COT')
= tan1 ()
WT'
(27)
T
Ys
Xc
(28)
/
(28)
A
where
c
EA
)C~~~
()cs^(O
(29)
)
W
13
I
_ I
____1_1_··^
·_1__________·__1___^lL_ll__·_
·1_--111--Ll
·-
...-._-_.-_ .-11111111
_ -
- ---
I
=
E
Y(o) sin
oW(T+Tl)
(30)
XC =
E
X(X) COS aw(To+TI)
(31)
X(O) sin AO(TO+TL).
(32)
Y
Xs =
The exact expressions for A and
small when
analyzed.
Wo(TVo+rI)
wTy'
involve a large number of terms that are very
undergoes a change of a few radians over the bandwidth that is
When a 1-bit correlator is used only the normalized power spectrum is
obtained, so that it is impossible to obtain any fringe amplitude and phase information
o+rI) is large enough to produce many fringes across the bandwidth.
Note that if the summation over w is done first, then in the case of a white-fringe
unless A(
compensated system (O(T+T
)<<l). the method is equivalent to a least-squares fit to
the time-function output of an integrator preceded by a square-law detector and filter
with a bandwidth of Aw/2rr
3.4 NORMALIZED AUTOCORRELATION FUNCTIONS AND POWER SPECTRA
FROM THE DIGITAL CORRELATOR
A Weinreb digital autocorrelator was used to obtain the fringe amplitude and phase
information from the combined IF signals.
1
The normalized autocorrelation function
correlation function
bution for the signal
p
(T)
p(T)
is obtained from the clipped-signal auto-
on the assumption of a Gaussian bivariate probability distri-
2
(33)
p(T) = sin 2 PC(T).
The difference of normalized autocorrelation functions for the added and subtracted IF
signals is given within 1% for most signals in radio astronomy by
Dk,t
(Ak, t-Bk, t+100 msec)r
A
1,t
k=1, ...
(34)
100.
Ak, t and Bk, t (regarding positive signal as logical 1 and negative signal as logical 0)
are the counter output numbers for the added a subtracted signals, respectively. The
subscript k designates the delay number (1, ... 100 for the Haystack correlator).
k = 1 corresponds to zero delay and consequently is just the number of samples
in the integration period.
This approximation to the clipping correction was made to
save computer time.
14
_
__
____
_____
____I
The normalized difference power spectrum is obtained by taking the Fourier transform
100
D,t()
1
Wk =+
100
[2rrZ(i-1)(k-1l)
2E
wkDkt Cos L
400
k=2
1
cos
i=1, ...
200
(35)
7(k- 1)
100
(36)
where wk is a cosine weighting function, and i is the frequency channel number. Usually
only channels 21 to 181 are used, as these are limits where the bandpass function
starts to drop.
The frequency offset 2A is given by
(i- 101)2TrBW
ha =
160
'
(37)
where BW is the bandwidth between channels 21 to 181, a quantity available to the U490
computer via the data coupler. The filter section before the correlator is designed so
that channel 101 corresponds to 30. 0 MHz in the IF spectrum.
The power spectrum is converted to a temperature scale by multiplying by the system
temperature and dividing by the normalized power spectrum of the noise entering the
clipper. This is an approximation that only holds for signal power much less than
receiver noise power.
The power spectrum obtained without knowledge of the signal
power integrated over the bandwidth has a zero as the average value of the spectrum.
The effect of this on the interferometer data is to produce an apparent fringe phase in
portions of the spectrum where there is no signal. In practice, the effect is small, but
it can be taken out of the data with a knowledge of the spectrum from single-antenna
The exact expression for the difference spectrum in °K is given below.
measurements.
SBp(i) SDi)t(i)
= Sn, t(i)(Ts+Rx,t( 0 ))-
Sn,t,(i)(Ts+Rx,t,())
(38)
- TS(Sn t(i)-Sn, t,(i))
(39)
for
Rx,t(i), Rx,t(i)
0,
where SBp(i) is the bandpass function of the radiometer, Rx,t(0) and Rx t(O) are the signal temperatures at time t and t', respectively, averaged over the bandpass. Sn,t(i)
and Sn t,(i) are the Fourier transforms of sin 2 c t(T), and Pct,(T). The approximation made to this expression only holds for continuum sources when there are many
fringes across the bandwidth as we have mentioned.
3.5 SYSTEM CALIBRATION
The normalized fringe amplitude of a point source or of one that is not resolved by
the interferometer is defined to be one. If it is not possible to make measurements with
15
I_ _
_ _I _
_
zero spacing, it is necessary to calibrate the interferometer.
There are two methods
of calibration, both of which may be useful, the choice depending on the circumstances.
The first method is to use measurements made with each antenna and radiometer indiThe individual radiometers are calibrated and the system temperatures meas-
vidually.
If the proportion of power from each radiometer is
ured.
B, then the radiometer signals
added can be written
4_0- fA
4
1 S1
S (t)++
l (t )
~B
f nl~t)/TA
n (t) +
S 2 (t) + n 2 (t),
(40)
fT~A2
S 2 (t) - n 2 (t),
SZ
(41)
1
Si
and the subtracted signals as
-TA 1
Sl (t ) + F
NfSi
7
n(t) -
where Si(t) and S2(t) are the power-normalized signal time functions, and nl(t) and n 2 (t)
are the power-normalized receiver noise time functions.
Since nl(t) and n 2 (t) are uncor-
related,
TS
(3+1)
2
(42)
TS2 '
1 51TS
where T S is the over-all system temperature,
TS1 is the system temperature of
receiver 1, TS2 is the system temperature of receiver 2, and
power level from receiver 1
=power level from receiver 2'
With the system temperature defined in this manner, the fringe amplitude in
K cor-
responding to a normalized fringe amplitude of one (a point source) is
2-
(43)
NTA1lTA2
where TAl and TA2 are the individual antenna temperatures.
normalized by dividing this expression.
Fringe amplitudes can be
In order to optimize the signal-to-system tem-
perature ratio
4
~/TA1TA2
4PSTS2TA ,
[+1 siTs2
the ratio3 is chosen so that p = 1,
(44)
or the power levels
are weighted equally.
When this is done the signal-to-system temperature ratio becomes
2
AlTA1TA2
TS1 TS2
16
The second calibration method involves no system parameters and no calibration
noise sources. The procedure is to measure the power spectrum of the source from each
antenna while keeping the other just off the source.
the measurement.
Loading switching is used to make
[The phase switching may be stopped and the signals just added, since
the phase switching clearly has no effect in this mode.]
If the signal were originating
from a point source, then the fringe amplitude would be
{(S 1(W)+
A(a)) =
= 4 S l (c0)S
2))
(o)
2 (c),
where S(w) and S2(c)
(46)
are the spectra from each antenna,
with load switching used.
Fringe amplitudes can thus be normalized by dividing by 4 4S1 ()S
2
().
3. 6 DISTRIBUTION OF BRIGHTNESS TEMPERATURE AND SOURCE POSITIONS
FROM FRINGE AMPLITUDE AND PHASE
The fringe amplitude and phase provide information on the source distribution. For
a general spatial distribution of incident flux, under the assumption of statistical independence of the plane waves that make up the expansion, the brightness temperature distribution and complex fringe amplitude are related by the following transform pair
Ak, (w) e
SAk()
~
ek
= 4i
ST B(C x, y) e
eikx eY
dkd
4r
=2
e
JqG
1
(w, x, y)G2 (c, x,y) dxdy
Gl(,x, y)G2(w, x,y) TB(o,
,y),
(47)
(48)
where TB(O, x, y) is the brightness temperature at a point located at a distance x parallel
to the direction of increasing Right Ascension and a distance y in Declination from the
reference point.
G 1 (c, x, y), G 2 (, x, y) are the antenna gains which may be taken outside
the integral, in most instances, when the region mapped with the interferometer is much
smaller than the beam patterns.
k and
are the spatial fringe frequencies and are the
coordinates of the transform or fringe-amplitude plane.
aYTt
k-
ax '
aOT't
=
ay
(49)
A plot of the coverage of the fringe-amplitude plane for the fixed-baseline Haystack/
Millstone interferometer is shown for several sources in Fig. 9.
For a fixed baseline interferometer,
t
D {sin B
so t that
in 6s+Cos
B cos 6S cos (Ls-LB)},
so that
17
(50)
6
k = N cos
(51)
B sin (LS-LB)
= N sin 6B cos 6S- N cos 6B sin 6S cos (LS-LB)
(52)
where
LS = Hour Angle of the source
LB = Hour Angle of the baseline
S
= Declination of the source
6B = Declination of the baseline
N = Number of wavelengths in the baseline.
The brightness temperature can be obtained by taking the Fourier transform of the
Unfortunately, a fixed-baseline interferometer
fringe amplitude and phase function.
N
Fig. 9.
Fringe-amplitude phase coverage for some
OH sources. The limits shown are the
observable limits.
E
w
has a very limited fringe-amplitude plane coverage, so that the transform analysis is
not always used. Instead, the fringe amplitude and phase of certain model distributions
are noted and compared with the observed fringe amplitude and phase.
the normalized fringe amplitude of a uniform disc of radius R is
were
JrS
For example,
fr)
RiT/S
where J1 is the first-order Bessel function, and S is the fringe spacing.
1 = k2 +
S2
2.
(53)
The fringe phase for a disc is
18
WT'
= DC [(sin 6B cos 6S) A6S+ (cos 6 B co
R. A.
A
S sin (Ls-LB))
S
(54)
- (cos SBsin 6Scos (LS-LB)) as]
where
A6 S = offset in Declination of center from the reference position
AR. A.S = offset in Right Ascension of center from the reference position
D = length of baseline.
The relations above are used to determine the position and effective source size limit
when a source shows no amplitude variation with hour angle, other than that expected
from the noise.
The source position is determined by making a least-squares fit of the
phases to an offset in position.
Other distributions that have simple fringe amplitude and phase functions are a
double source which is given by vector addition of the vectors representing the complex
amplitudes for the two point sources, and circularly symmetric sources which have
zero phase.
3.7 COMPUTER PROGRAMS
Data processing for the Haystack-Millstone interferometer was done in two stages.
First, a real-time data-processing program in the Univac-490 computer recorded autocorrelation functions on magnetic tape, together with timing and antenna pointing information, and provided a monitor on the operation of the system.
The contents of this
tape were then analyzed, at some later time, by a Fortran program on the CDC 3200 to
derive fringe amplitude and phase.
a.
Real-Time Program
For this experiment, the Haystack and Millstone antennas were controlled simul-
taneously by the Haystack Pointing System 3 in the Univac 490 computer.
includes an on-line spectral-line data-processing program,
4
The system
which was modified to allow
the recording of autocorrelation functions from the digital autocorrelator at the rate of
1000 15-bit words per second.
This option may be requested by the observer via the
console typewriter, and does not interfere with the normal functioning of the program.
Interleaved with these data records were partial system data records, which contain
command pointing angles (in both celestial and horizon coordinates), computed refraction
corrections, and time.
b.
Fortran Fringe-Processing Program
The tape written in
real time was processed by using a Fortran program.
19
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20
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DEG
12
reference phase was computed by using the equation given in the section on interferometer geometry.
The phase and amplitude were determined by the least-squares
filtering technique discussed here.
in Fig.
10.
An example of the high-speed printout is shown
The Fortran statement of the program is given in the appendix.
21
IV.
INTERFEROMETER NOISE ANALYSIS
The difference spectrum SD t(
)
for a sample of length At is made up of Gaussian
noise from the two receivers plus signal noise.
The receiver noise waveforms are
assumed to be uncorrelated, while the signal noise is correlated.
SD, t()
= A(X) cos +(c)
+(X)
oT
cos
WoTt
- A(X) sin +(o)
sin
o t + Nt(,),
(55)
where
=
(56)
+ AW(Tt+) (Tt+'(().
+
After digital filtering for a time T, during which cos wovt goes through many cycles,
X(w) = PA(X) cos +(M) + Z Nt(w) cos WoTt
t
Y(o)
=
since Z sin
-QA(w) sin 4(w) + Z Nt sin COT
t
oVt cos W0Ot
t
}
(57)
Quantities defined in Eqs. 19-22
(58)
0.
The signal and noise can be represented as the sum of two vectors
R = A + N,
(59)
where
A = A(X) cos
(X) ix + A(c) sin +(w)
Z Nt(o) sin
Z Nt(w) cos ~Oo-Tt
N =
-
iy
i-P
-t
(60)
%oTt
iy
Q
(61)
where IR is the estimate of fringe amplitude.
The noise vector has uncorrelated components, since
t
Nt(w) cos
t
oTt
N
.L
c c
±O
t
s
Nt(w) sin
r s
Oot
i n
ot T
oOTt
(62)
0.
Assume that Nt(w) Nt+At(w) = 0 and 2 cos ot sin wot = 0, which is a good approxit
mation for long integration times. Nt(c) is a Gaussian random variable so that the components of N are independent Gaussian random variables with zero means and variances,
2 . Joint probability distribution of the components is
(a 2x +a2)
y!
20- 2
1
P(ax,
ay) =Z
e
2
(63)
22
where
e
(64)
N I sinO
(65)
ax= |N| COS
ay=
so that (see Fig. 11)
-2(67)
1<2
Fig. 11.
Signal and noise vector.
The variance a-2 can be computed from the variance of Nt(w)
2
2
Z Nt(O ) cos
t
cos 2
COoTt
t)
2
At 2 Nt(w)
a TS8
(68)
/
T1
where Af is the frequency resolution of the spectral measurement, (a) is a factor that
normally is unity but equal to approximately 1. 3 when the Weinreb correlator is used
for spectral measurement. The additional factor of 2 arises from the fact that the difference spectrum is obtained by subtraction of two independent spectra,
with integration time At/2.
The length of the noise vector has a Rayleigh distribution with mean
7 aT 2 4ZT
a'J =S /2
a
Z(69)
as shown in Fig. 12.
23
each made
1z
IL
Probability distribution of the amplitude of the noise vector.
Fig. 12.
The rms deviation of the amplitude and phase of the estimator is easily computed
only for large signal-to-noise ratios when
INZ
II12= IA 2 +
(70
))
IRi IAI
(71
and therefore
4aT
12)
(
A rm
~
==
NI
I
rms
2
2
OK
(r -S
(72)
\1/2
sin2 0
12
=
=
IAI
- radians,
(73)
A TfT
where A is in °K.
For any signal-to-noise ratio,
2 T
rms
=
h~rms
O
(an
INI sin 0
E1
y
cos
IAI + I Cos ;
2
a
2
2
e
dedINI
(74)
which reduces to the expression above for large signal-to-noise ratios.
)
/
In practice, signals weaker than (
cannot be distinguished from the noise,
and it is fairly reasonable to consider this to be the interferometer threshold. Figure 9,
showing a plot of fringe spectral amplitude and phase, clearly illustrates the signifi-
cance of the threshold.
24
The interferometer threshold can be reduced by using other schemes of processing.
It will be shown that the system used here is a factor of 2 from optimum.
The antenna
signals for a point source can be considered for the purpose of this discussion. Signals
from a more complex source are assumed to be the sum of uncorrelated components.
The output of the two receivers can be written
x(t) =
A
T S nl(t)
S(t) +
1
y(t) =
/A
(75)
1
S(t+)
+ 4T
2
nz(t),
(76)
2
where the function s is assumed to remain constant during the correlation time At. The
spectrum of the receiver noise is assumed to be unity over the bandwidth considered.
Spectral information is contained in the autocorrelation functions
t'
<x(t)X(t-T) > e- i
H_
where S
c
T dT =
TA S(o) + T
(o) is the noise in the measurement.
+T
S
(),
(77)
The angular brackets denote time
1
averaging over the integration period.
Cross terms are omitted, under the assumption
that the signal power is much less than the receiver noise.
S
()
= 0
(78)
1
SnliM=
1
(79)
where Af is the spectral resolution, and S 2 (co) is the variance of spectral measurement
n1
derived under the assumption of Gaussian statistics for the noise. The information about
t
is contained in the crosscorrelation function,
2
<x(t)y(t-T)
+
TS TS
> e
dT = 2Z
/
A
(Re Sn(W) + iIm Sn()),
- io
e
S(A)
(80)
where the real and imaginary parts of the cross spectral function Sn(w) will be shown to
be independent noise terms.
The factor of 2 is introduced to make the signal equal to
2 a/ T
are the average antenna temperatures over the bandwidth
T
T
and T
1 A2
1
2
considered. That is,
TA(o) 2r
J--ob
=
. TAS(
S("
2r
TA.
TA
25
(81)
The independence of Re S n(C) and Im S n()
can be proved by showing them to be
uncorrelated.
Re Sn(w) Im Sn(o)
(nl(t)n 2(t-T)
=
=
SS (n
l(
( nl(t')n2(t'-'))
t)n l (t' ) )(n2(t-T)nZ(t'-T'))
sin crT COS wT ddT'
sin
wTr cos w-Tr dTdT'
0.
(82)
To find the variance of Re Sn(o) and Im Sn(w), consider the variance of the terms in the
spectrum of added noise
i,'
K(nl(t)+nz(t))
Sn(o
)
((nl(t-T)+n 2 (t-T)) e-iT dT
+ Sn2(c) + Re Sn(o) + i Im Sn(o) + Re Sn(c) - i Im S().
(83)
t because adding the
The variance of the spectral estimate for the added signal is
uncorrelated Gaussian signals gives a Gaussian signal with twice the power.
Var
Thus
(84)
Re Sn(A)] -=
Snl ()+Sn2(c)+Z
Clearly,
The individual terms are independent.
S
(o) and S
(c) are independent.
Sn (w)and Re S n(c) can be shown to be independent in the following manner.
Re
5
n(
n1 -
)
n 1(t)nl(t-iT))
SS
(nl(t)n2z(t'-T)) cOs
Tr os
Tr'dTdTr'
it'nlZ(')n(t'-'))
= SS ( (nl(t)nl(t-T))
+ (nl(t)n (t')) (nl(t-T)n 2(t'-T')>
+ (nl(t)n2(t'-T'))
(nl(t-T)n 2 (t')))
cos
CyT COs
T
ddT'
(85)
= 0,
since n
and n 2 are independent.
Var[Sn (c)+ S
()+
Therefore
2 Re Sn(c)
=
Var S
()
+ Var S
()
+ Var 2 Re Sn(o),
(86)
so that
Var Re Sn(W)
=
1
2fAt'
(87)
26
~0)~~~~~~~C
§
C
Uc
~o
0
X
(.
U,
--
I.
UU
*,(
,
d)
C
G
l
E
EE
c
>
2e
)
i ,O
0}
0)
>,,
CD
~
p,
C
L
0.0,
E
CN
E
"U
E
-
>-0
H
C~~~~~~~~~~~~~~~~~~~~~(
H
(N
Co
Q:.
>'
x
,v
C)
N
CN
0)
+
I
r.>
0
x
+1
0)
0
x
x
0)c,
.Q
C)
E
a)
Se
X
-Iq
X
>
D
Vt..-
_tEE
.
98~~~~~~~~~~(
E
X
x
x
x
o 2
Cn
2
2E
o
c~)
"
27
__III_1__ ·_l----l_^.pl
I
-·-
-------
·I^
The variance of Im Sn(w) is the same as the variance of Re Sn(w).
by introducing 90
°
Then
phase shift in x or y.
2 x(tfa)y(t-T)=
2i e-i
e1
TA T
= 2
dT
This can be shown
:
(x(t)y(t-T'
S(w) + 2TT
ew
e
dT'
(88)
(-ImSn(o) + iRe Sn())
Ifthe crosscorrelation technique were applied to the signal from one antenna it would
have an rms of N-times the rms for a total power radiometer. This is seen by setting
4 = 0, and considering only the real part of the transform. The signal is TA, and the
TS
. The factor of two is dropped for the signal, because of the 3 db lost
A-fAt
in the division of power to the two receivers. When crosscorrelation is used to deterrms noise
mine
TA TA S(w) e- i
2
1
and S(o), the signal vector is 2
has components 2
T
T
Re S ()
and 2T
2 4 _2
S TS
c
and the noise vector, which
+
ImSn(), each with variance t
T
2
(from Eq. 72). The averaging or filtering
thus has an rms deviation of
N1Jf At
of the crosscorrelation functions to take out the time-variant component (resulting from
Wct
the earth's rotation) of
is accomplished by multiplying by e
and summing.
This is
equivalent to the least-squares fit technique, but is much simpler, owing to the existence of the imaginary component.
The crosscorrelation function contains all the fringe information and the best estimate of this function must be the optimum system.
It might be questioned whether it is
the optimum scheme when it is clear that even if we know the fringe phase in advance of
the source position and want to estimate the source flux, the system has
than a total power radiometer which is known to be optimum.
I- more noise
If measurements of flux
are to be made, however, with a total power radiometer, half the observing time should
be spent determining the receiver noise power. The increase of - in the noise of the
crosscorrelation estimate is offset by the added information (receiver noise has been
subtracted out) in the crosscorrelation function. Table 1 shows various interferometer
detection schemes and their noise thresholds.
should be noted.
One disadvantage of crosscorrelation
The spectral resolution obtainable with a crosscorrelator is half that
of an autocorrelator with the same number of delays. The reason is that crosscorrelation
functions are not symmetric, and require both positive and negative delays to extract the
available information.
28
POLARIZATION ANALYSIS
V.
An interferometer can be used to analyze the polarization of a radio source. A complete set of polarizations can be obtained from the autocorrelation functions of two
orthogonal polarizations plus the complex crosscorrelation
function between the two
For right, left, and two sets of linear equations, we have
polarizations.
ZSR(cO) = SH(O) + SV(w ) + 2 Im SH, V(O)
(89)
ZSL()
(90)
= SH(w) + Sv(o) - 2 Im SH,
(91)
+ SV(w) + 2 Re SH,V(w)
2S 45 o (W) = SH()
2S_45o(W ) = SH()
+ SV(O ) - 2 Re SH,V(w)
(92)
where
S(o)
R(T) e-
=
(93)
T dT.
-oo
These relations are derived from the autocorrelation functions.
0
4IT xR(t) = xH(t) + xv(t+9 );
For example,
(94)
therefore,
2R
xR
(T) =
R
x
(T)
+ R
x(
xHxVR(-90)
xx
() +
+ R
x(x
(-T-90°)
(95)
and hence
(96)
2SR(MO) = SH()) + Sv(O) + 2 Im SH, V(O).
When both elements of the interferometer have the same polarization, the autocorrelation
function is measured.
For example,
oo Rx
dT = e
(T-%)
e
(97)
SV(w)
When the interferometer is used with elements having orthogonal polarizations the
crosscorrelation function is obtained but real and imaginary parts of the Fourier transform can only be separated from the fringe phase information by making measurements
with polarizations exchanged.
oo
(T--)
,
-k(Rx
TSH,=eV(+)m
{Re
V(W) + i Im
(98)
while
+00
9
Rxx
oo
(T-0
RH(
e
e
1WT dT =Wo
e, -
fRe SH V(O) - i ImSH V(O)}.
Vd=
)
29
(99)
For an extended source, both of these measurements are required to obtain the
polarization parameters over the source distribution. With the use of vertical and horizontal polarizations as an example, the Fourier transform of the fringe amplitude for
vertical polarization yields the distribution of vertical polarization, and similarly for
the horizontal polarization, while the distribution of right minus left and +45 ° polarization minus -45
°
polarization are given by the transform of the sum and difference of
complex amplitudes made with one element of the interferometer vertical and the other
horizontal, and vice versa.
30
VI.
CONCLUSION
This report shows that while a digital correlator (with phase switching), or a digital
crosscorrelator, is useful for a spectral interferometer it also has many advantages
when spectral information is not required. It is interesting to note that the optimum
receiver system for making a radiometric map as a function of frequency and polarization, with two single-feed antennas used, consists of 4 receivers and 4 crosscorrelators:
one receiver on each of the two orthogonal polarization ports of each antenna,
and the crosscorrelators between pairs of receivers, one on each antenna.
31
_
_
II
ICICI·_
_L
_
__I__ __11
_11____1_
_·
APPENDIX
Fortran Statement of the Program
3200
(2.1)
FORTRAN
PROGRAM MILSTAK
DIMENSION CT(400),WKlOO),F(241B),T(241B),ASUM(200) SC(3108).
1 PAR(238),NH(102) ,ISUM(2o,100.),AZS(6)TIME(6),ELS(6),PH(6),
2
PwREF(5),X(100),Y(100)XT(200)YT(20O),PHASE(200),
3 AMP(200),CPR(5),SPR(5),TITLE(/1),PA(80),ANS(lO),PHA(200),
4 LABELX(6),LABELY(8), KI(4),TIT(21)
5 INFO(364),PNH(lO2)bU(100),Z(100),TRANS(200),NHT(28)oCP(5),SP (5)
COMMON ISUMS,DPHA,PHASE
CHARACTER PA,PNH
EQUIVALENCE (NN.PNH)
INTEGER TITLEREPLYTITOT
PIF=3.14i5926536
C
C
R=3.141592653/180.
PEAD 1,DMIL,DBASELB,AZB
1 FORMAT(4F10.4)
CER=COSF(ELB*R)
SER=SINF(ELB*R)
STORING TABLE FOR FOURIER TRANSFORM
DO 78 I=1,400
78 CT(I)=COSF(2.*3.i41592653*( I-1)/400,)
t'K IS WEIGHTING FUNCTION FOR ATOCORRELATION FUNCTIONS
DO 17 Kl,100
17 WK(K)=.5+.5*COSF(C3,14159*¢K-1))/100.)
900 INUM=O
WRITE(59,955)
955 FORMAT(37HNEW OUTPUT TAPE REQUIRES JUMP SW 2 ON)
PAUSE
ISRCH=3
99 CONTINUE
GO TO (928,929) SSWTCHF(.2)
928 WRITE(59,930)
930 FORMAT(14HMOUNT NEW TAPE)
PAUSE
GO TO (961,929) SSWTCHF(2)
961 LND FILE 20
REWIND 20
929 CONTINUE
INUM=INUM+1
DO 77 11,5
77 TIME(I);86400.
DO 18 K,100
Y(K)O.
tl
( K) O
18 )(K)O.
IREP=O
IMISCO
IT=0 .
PP=O.
Q:0=O.
RR=O.
GO TO (3.3.119,184
ISRCH
32
--
-
----
-----
184 ISRCH*2
GO TO 119
C
READ INPUT PARAMETERS
119 WRITE(59,120)
120 FORMAT(28HTYPE T FOR CLIPPED TRANSFORM)
READ(58P121) OT
121 FORMAT(A1)
WRITE(59,101)
101 FORMAT(31H CENTER FREQUENCY IN MEGACYCLES)
READ(58, 102)PA
102 FORMAT.80R1)
CALL NUMIBERS(PA.80,ANS,NA)
IF(NA ) i.03,104,103
103 FREO=ANS(NA)
104 WRITE(59,105)
105 FORMAT(47HINST PHASE IN DEGREES AND DELAY IN MICROSECONDS)
READ(56106 )PA
106 FORMAT(80R1)
CALL NUMBERS(PA8'O,ANS, NA)
IF(NA)108,109,108
108 PINST=ANS(NA-1)
DE AY=ANS(NA)
109 WRITE(59,110) FREQPINSTDELAY
110 FORMAT(4HFREQFl0.4,12HMC/S INST PH,F8.3*llH DEG DELAYF9.3,9H MI
ICROSEC)
WRITE(59,112)
112 FORMAT(5HTITLE)
READ (58,113) TIT
113 FORMAT(14A4)
IFtTIT EQo. 1H )123#124
124 DO 125 I1,21
125 TITLE(I)=TIT(I)
123 WRITE(59,114)
114 FORMAT(6H HAPPY)
READ(53,115) REPLY
115 FORMAT(A2)
IF(REPLY.EQ. 2HNO) 119,116
116 CONTINUE
WC=FREQ*12.*2.5400 0506/2997929
W;WC*DBAS
C
C
C
C
C
C
C
C
3 CALL INFREAD(F,T,ASUM,SC,PAR,NH,MODENINTNBW, ISUMNC)
NC
-1
PARITY ERROR
0
END OF FILE
2
TITLE
1
GEO.RGEXS PROGRAM
3
PARTIAL SYSTEMS RECORDING
5
CHANNEL 5
CHANNEL 6 (AUTOCORRELATION FUNCTIONS)
6
NC=NC*2
GO TO (100,300,200,400,50000,00700,800,600) NC
600 GO TO 3
400 CALL ICVT(2,19,KI°l1)
KI(l)KI(1)-1900
DO 401 1=1,28
401
NHT(I)=NH(I)
GO TO 3
33
100 WRITE(59,199)
199 FORMAT(23H PARITY ERROR, PRESS GO)
PAUSE
GO TO
SRCH
500 GO TO (3,534,529)
529 K;HOUR=PAR(3)/3600.
NMIN(PAR(3)-NHOUR*3600,)/60.
NSEC:PAR(3)-NHOUR*3600.-NMIN*60,
WRITE(59,530) NHOUR#NMINNSEC
530 FORMAT(14,6H HOURSI4,4H MIN,I4*4H SEC)
WRITE('59531)
531 FORMAT(33H TYPE 1 SKIP. 2 PROCESS, 3 REINIT)
READ (58,532) ISRCH
532 FORMAT(I1)
GO TO (3,534,119) SRCH
534 DO 501 L=1,5
=6-L
AZS(M+1)=AZS(M)
TIME(M+1)=TIME(M)
ELS(H+)=ELS(M)
501 PH(M+1)=PH(M)
SOURCE COORD
C
AZS(l)=P4R(1)
ELS(1)=PAR(2)+PAR(4)
TIME(1)=PAR(3)
CES=COSF(ELS(1))
SES=SINF(ELS(1))
COMPUTE REFERENCE PHASE PH(I)
C
PH(1)=2.*3.141592653*WC*(DBAS*(SEB rSES*CEB*CES*COSF(AZS(1)-AZB*R))
1 -DMIL*CES/12,)
PASC=PAR(5)
DECL=PAR(6)
C0 TO 3
700 IF(MODE)3,701.3
701 PW=NBW
PW=BW/1000,
GO TO (702,3) SSWTOHF(5)
702 ISRCH=4
GO TO 99
C
********+t*********++6*+++
C
C
800 GO TO (3,880,3)'ISRCH
880 IF(MODE)3,809,3
809 DO 802 1=2,6
IF(PAR(1)-86384,)803.3,3
803 IF(PAR(1)-TIME(I))802802818
802 CONTINUE
GO TO 3
818 DO 816 J=1,4
IDIF=(PAR(J*l)-PARJ))*40.*,5
IF(IDIF"8) 817,816,817
817 IMISIMIS+1
816 CONTINUE
DO 815 J=1,5
,811
IF(ISUM(1,1,J))811 3
COMPUTE REF PHASE AT TIME DATA IS TAKEN
C
811 PHREF(J)=PH(I)+(PHC(I-i)PH(I))*(PAR(J)TIME(I))/(TIMECI I)-TIMECI)
1)
34
SPR(J)=SINF(PHREF(J))
CPR(J)=COSF(PHREF(J))
PP=PP*CPR(J)**2
OQ=Q4*SPR(J)**2
PR=RR+CPR(J)*SPRCJ)
815 CONTINUE
IT=ITI
IF(IT-1) 806,807, 806
807 P1=PHREF(1)
Ti=PAR( 1.)
1HI=PAR(1)/3600.
IMI=(PAR(l)-IH1*3600)/60,
ISl=PAR(1)-IH.l3600.IM
*60
XINT=(PAR(1)-TIME(I))/(TIME(IC-TIME(I))
A1=(AZS(I)*(AZS(I-t)-AZS(I))*XINT)/R
EI=(ELS(I)+(ELS(I-[)-ELS(I))*XINT)/R
C
SUM PRODUCTS OD AC FUNCS AND COSINE AND SINE OF PHASE
806 IF(OT E., 1HT) 840.841
840 DO 842 J=1,5
DO 842 K=1,100
842 U(K)=0.
841 DO 808 J=1,5
CP(J)=CPR(J)*PIE/ISUM(lfi,J)
SP(J)=SPR(J)*PIE/ISUM(1,1,J)
DO 808 K=1.100
DX:ISUM(1,K,J)-ISUM(2,KJ)
X(K)=X(K)+DX*CP(J)
808 Y(K)=Y(K)*DX*SP(J)
T2=PAR(5)
A2=(A7S(I)+(AZS( I-)-AZS(I))*(PAR(5)-TIME(I))/(TIME(I-1)-TIME(I)))
1/R
E2=(ELS(I)*(ELS(I-1)-ELS(I))*(PAR(5)-TIME(5))/(TIMECI-1)-TIME(I)))
I/R
GO TO 3
C
*+*
*w*****.**
*******
*************
*****
***~+*~+
C
C
300 WRITE(59,301)
301 FORMAT(11HEND OF TAPE)
REWIND 30
PAUSE
GO TO 900
200 GO TO (279,204,279)ISRCH
279 ISRCH=3
GO TO 3
204 P2=PHREF(5)
IH2=T2/3600.
IM2=(T2,IH2*3600,)/60.
C
IS2=T2-IH2*3600-IM2*60
LOCAL HOUR ANGLE
MH=PAR(5)/3600.
YM=(PAR5i-MH*3600, )/60,
MS:PAR(5)-MH*3600. MM*60,
AZIM=(A2+A1)/2,
ELEV= (E2+E1) /2.
FR=(P2-P1)/(2.*3.1415926)
DO 209 I=1,100
U(I)=U( I )/( IT*5, )
X(I)=X(I)/(IT*5, )
'209 Y(I)=Y(I)/(IT*5,;
35
--
*3
"
-------- ·- · IIIIL-
---
--
---
-----
-
C
COMPUTE FOURIER TRANSFORM
DO 203 11,200
XT(I)=O.
YT(I)=O,
TRANS(I)DO.
DO 203 K=2,100
N=(I'l)*(K-l)-((I-')*(K-l)/400)*400*1
TRANS(I) = 2.*U(K)*WK(K)*CT(N)*TRANS(l)
XT(I)=2.,X(K)*WK(K)*CT(N)+XT(I)
203 YT(I)=2,*Y(K)*WKCK)*CT(N)+YT(l)
DO 205 I=1,200
XNUM=RR*XT(I)PP*YT( I)
XDEN=QQ*XT(I) -RR*YT(I)
CALL ARCT(XNUM,XDEN,PHA(I))
TAU=(P2*P1)/(2.*FREQ)ODELAY*2.*3.14159
C
SUBTRACT INSTRUMENTAL PHASE WHICH IS FREO DEP
PHASE( I )=PHA( I )PINST.-I-101)TAU*BW/160.
IF(PHASE(I))220,222,221
221 NUMB=(PHASE(I)*3.141592653)/(2,*3,141592653)
GO TO 223
220 NUMB=(PHASE(I)-3.141592653)/(2,*3,141592653)
223 PHASE(I)=PHASE(I)/RaNUMB*360,
222 IF(PHA( I) )224,205,225
225 NUMB=(PHA(I)+3.141592653)/(2.*3.141592653)
GO TO 227
224 NUMB=(PHA(I)-3.141592653)/(2.*3.1 4 159k 6 5 3)
227 PHA(I)=PHA(I)/R-NUMB*360,
205 AMP( I )=SRTF( (YT( I )**2 ) * ( RR*2PP**2)*(XT( I )**2)*(**2+RR**2 ) 1 2.*XT(I)*YT(I )*RR*PP*QQ) )*( I'*5, )/(PP*Q-R**2)
C
AVERAGE PHASE AND AMPLITUDE FOR CONTINUUM SOURCES
YC=O.
XC=O .
YS=O .
XS=O.
DO 207 I=21,181
YC=YC*YT(I)*COSF((I101)*TAU*B6W/160 9 )
YS:YS*YT(I)S I NF ((I 11)*TAU*W/160)
XC=XC*XT(I)*COSF((IC101)*TAU*BW/160,)
207 XS=XS*XT(I)*SINF((I1101)*TAU*BW/160,)
XNUM=-YC-XS
XDEN=XC-YS
CALL ARCT(XNUM,XDENPCAL)
PCAL=PCAL/R-P INST
PAMP=SQRTF(OO*QQ*(YC+XC)**2*PP*PP*(XCSYS)**2)*IT*5./(PP*00*161.)
C
C
C
*****
**********************************************************
LIST ALL POWER SPECTRA ETC
PRINT 286,( NHT(I),1=l,27)
286 FORMAT(1H1,3X,27A4,/)
PRINT 949,(PNH(I), I:,405)
949 fORMAT(1X,135RIe/,i X,135R1/,X.135R1j/)
GO TO (252,254) SSWTCHF(3)
254 PRINT 287
COSINE AUTOCORR
287 FORMAT( OX,66HF-REQUENCY
1 SUM AUTOCORR///)
PRINT 289,(I,X(I),Y(I),U(I)1I:=,100)
289 F ORMAT(lOX, I4,3F20,7)
PRINT 291
SINE AUTOCORR
36
I
I
I
_
_
_
2 IMIS,M*,MMMS,DECL
270 FORMAT(21A4,19H@ASELINE PARAMETERS,37X,6HLENGTH,FO,2,6H FEET,34X
1F166.2,12H WAVELENGTH,28X,9HELEVATION,F9.,,8H DEGREES,30X,
27HAZIMUTH,F11l.4,fH DEGREES,86X,5HDELAY,F18.3,5H MICS,28X,
310HINST PHASEF13.3,4H DEG,29X,9HFREQUENCYF14.4,5H MC/S.28X,
410HTIME START,314.
34X10OHAZ
STARTF13,3,33X,0HEL
START.
5F13.3,33X,lOHPH
START,F3.3,35X,10HTIME STOP,314,
34X,
610HAZ
STOP,F13.3J33X,lOHEL
STOP#F3,3*33xlOHPH
STOP,
7Fl3.333X,lOHFRINGES
,F13,3,33X,10HINT TIME *I10
.8H CYCLES,
856X,5HDATE 5X,314,34X,9HBANDWIDTH,F10.2,55H MC/S,32X,6HMISSES, 10,
940X,1OHLOCAL H.A,,3I4,34X,3HDEC,F12,4*4H DEG)
C
FLOT CSINE TRANSFORM
CO TO(910,251) SSWTCHF(3)
251 CO TO (90i,262) SSWTCHF(1)
901 IF(INUi.)233,262,237
262 WRITE (59, 230)
COS
230 FORMAT(29H SET FOURIER TRANSFORM LIMITS)
FEAD(58,102)PA
CALL NUMBERS(PA,80jANS,NA)
IF(NA)232,233,232
232 XTMAX=ANS(NA-1)
XTMIN=ANS(NA)
291 FORMAT(IH1,106H FREQUENCY COS TRANSFORM
SIN TRANSFORM
RAW P
1HASE
FRINGE AMPLITUDE FRINGE PHASE
SUM TRANSFORM//)
PRINT 290,(I,XT(lI)YT(I),PHA¢I)AMP(I),PHASE(I),TRANS(I),1ul,200)
290 FORMAT( 5X,I4,6Ft6.4)
GO TO 292
252 PRINT 293
293 FORMAT(20X, 93HNUMBER
FRINGE AMP
PHASE
NUMBER
FRINGE AM
1p
PHASE
NUMBER
FRINGE AMP
PWASE/)
DO 294 I=1,53
J: I+20
K=I+73
LtI'127
FRINT 253,J,AMP(J).PHASE(J).KAMP(K),PHASECK),LAMP(L),PHASE(L)
253 FORMAT(14XI12,Fll4,FlOIl2Fll4FO.12,F11,1lI12,Fl.4,FO0.)
294 CONTINUE
C
OUTPUT TAPE
WILL SPACE TO END OF FILE HARK
OUTPUT
292 CALL SEFF(20)
EACKSPACE 20
WRITE (20) U,X,Y,XTYT,TRANS,PNA,PHASEAMPKI Tl.T2 A2,A1,E2,E1,
1 FRITPCALAZB,ELBDBASFREOW;F,TASUMoSCPARNH,~WPINST,
2 TITLE.P1,P2,RASC,DECL
END FILE 20
FACKSPACE 20
PRINT 984
984 FORMAT(////)
PRINT 211,AZIM,ELEVPCAL,PAMP
211 FORMAT(lOX,12HMEAN AZIMUTH,F10.4,//10X,14HhEAN ELEVATION,F8,4//,
1 1nX,12HFRINGE PHASEFl0,4//,lOXo16HFRINGE AMPLITUDEF12.4.)
C
C
C
FNCODE VARIABLES WHICH APPEAR ON GRAPHS
ENCODE(24,268,LABELX)
268 FORMAT(1OX,14HCHANNEL NUMBER)
FW:ABSF(BW)
FNCODE(1 4 56,270,INFO)TITLEDBASWELBAZB,DELAY,PINSTFREQ,IHl.
IIMI,IS1,AEE1,PPIIH2,IM2IS2,A2oE2,P2#FRITokI(2)KI(3),KI(1),bW,
37
I-_I
-·L__
I-I
"I"U- ---I
I---
--PC"-
I·PLC-IIIII--^·1L_C.
LL^I-
-I
265 CALL LI'TS(1.10l.-1bU,1u. 3
DO 245 1=2,200,2
XX=I/2
YY=:PHASE(I)
245 CALL POINTS(XX,YY,1R*J1)
CALL GRIDS(1l.,10,1,0.,-60.)
FNCODE(16,285,LARELY)
285 FORMAT(4X,12HFRINGE PHASE)
CALL LABELS(LABELX,6,LABELY,4)
CALL GRAPHS(INFO,15,364,1)
IF(IREP)906,267,906
267 IF(OT
EQ. 1H )299272
272 '.RTTE (59, 273)
233 CALL LIMITS(l.,0ll XTMINXTMAX)
rO 242 I=2,200,2
XX=I/2
YY=XT(I)
242 CALL POINTS(XX,YY,IR*,1)
CALL GRIDS(1.,10.,XTMAX,-(XTMAX-XTMIN)/4.)
ENCODE(16,269.LABELY)
269 FORMAT(16HCOSINE TRANSFORM)
CALL LABELS(LABELX,6,LABELY,4)
CALL GRAPHS(INFO,15,364,1)
PLOT SINE TRANSFORM
C
CALL LMITS(1.,lOl0XTMINXTMAX)
rO 243 1=2,200,2
SIN
XX:I/2
243
280
C
910
902
264
235
236
237
244
282
C
YY=YT(I)
CALL POINTS(XX,YYIR*,1)
CALL GRIDS(i.,10..XTMAX,-(XTMAX-XTMIN)/4.)
ENCODE(14,28n, LABELY)
FORMAT(14HSINE TRANSFORM)
CALL LABELS(LABELX,6,LABELY,4)
CALL GRAPHS(!NFO,15,364,1)
IF(IREP)906,910,906
PLOT FRINGE AMPLITUDE
C-O TO (902,264) SSWTCHF(1)
IF(INUM-1)237,264,237
bRITE (59, 235)
FORMAT(28H SET FRINGE AMPLITUDE LIMITS)
PEAD(58,102)PA
CALL NUMBERS(PA,80,ANSNA)
IF(NA)236,237,236
AMAX=ANS(NA-1)
AMIN=ANS(NA)
AMIN#AMAX)
CALL LIMITS(1. ,lo,
rO 244 I=2,200,2
XX=I/2
YY=AMP(I)
CALL POINTS(XXYY,1R*I)
CALL GRIDS(1.,10.,AMAX,-(AMAX-AMIN)/4,)
ENCODE(16,282,LABELY)
FORMAT(16HFRINGE AMPLITUDE)
CALL LABELS(LABELX,6#LABELY,4)
CALL GRAPHS(INFO,15,364l)
IF(IREP)299,265,299
PLOT FRINGF PHASE
38
AMP
273 FORMAT(25H SET POWER SPECTRA LIMITS)
PEAD(5,1lO02)PA
CALL NUMBERS(PA,80jANS,NA)
IF(NA)274,275,274
274
TMAX=ANS(NA-1)
TMIN=ANS(NA)
275 CALL LIMITS(1.,lO1,,TMINTMAX)
DO 276 I=2,200,2
XX=1/2
YY=TRANS(I)
276 CALL POINTS(XX,YYR*,1)
CALL GRIDS(.,10.,TMIN,-(TMAX'TMIN)/4)
FNCODE(13,277,LABELY)
277 FORMAT(13HPOWER SPECTRA)
CALL LA9ELS(LABELX,6,LABELY,4)
CALL GRAPHS(INFO,15,364,1)
299 r-o TO (905.906) SSWTCHF(1)
905 ISRCN=2
GO TO 99
IREP:O,NO REPLOT,1 COS AND SIN TRANS, 2 COS AND SIN TRANS,
C
3 FRINGE AMPLITUDE 4 SUM TRANSFORM
C
906 WRITE (59, 295)
295 FORMAT(12H REPLOT lg4 )
READ(58,296) IREP
296 FORMAT(I1)
IREP=IREP+l
GO T0(261,262,262,264,267) IREP
261 CONTINUE
WRITE (59, 969)
969 FORMAT( 41W JUMP SWITCH 1 ON FOR NON STOP PROCESSING)
PAUSE
GO TO (905,970) SSWTCHF(1)
970 WRITE (59, 278)
3 REINT AND SKIP, 4 REINT AND
278 FORMAT(63HTYPE 1 SKIP, 2 PROCESS
1PROCESS)
READ(580297) ISRCH
297 FORMAT(I1)
GO TO 99
END
3200 FORTRAN DIAGNOSTIC RESULTS - FOR
ERRORS
39
_
---------------· III·Il----.l----r.
-r^--r^r^--r-------r---l
-
^--------ru·-r----r_--r
MILSTAK
Acknowledgment
The author is grateful to a large number of people who contributed to this work. J. M. Moran, Patricia P. Crowther, and
J.
A.
Ball wrote the computer
programs.
G.
M.
Hyde,
V. C. Pineo, and J. C. Carter provided engineering assistance.
R. H. Erickson, R. Lewis, and D. C. Papa constructed much
of the equipment.
The author is particularly indebted to Pro-
fessor Bernard F. Burke who initiated the project and provided
much of the theoretical and practical knowledge.
Finally, the
author is indebted to Professor Alan H. Barrett for supervising
this work as a portion of thesis research that is being undertaken at the Massachusetts Institute of Technology.
40
----
---
I
References
1.
S. Weinreb, "A Digital Spectral Analysis Technique and Its Application to Radio
Astronomy," Technical Report 412, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Mass., August 30, 1963.
2.
J. H. Van Vleck, Report No. 51, Radio Research Laboratory, Harvard University,
Cambridge, Mass., July 21, 1943.
3.
F. E. Heart, A. A. Mathiasen, and P. D. Smith, "The Haystack Computer Control
System," Technical Report 406, Lincoln Laboratory, Massachusetts Institute of
Technology, Lexington, Mass., 27 October 1965.
4.
G. H. Conant, "Radiometric Spectral-Line Processing in the Haystack Antenna
Pointing System" (in preparation for publication).
41
I--I-LIUYW-I·PY*···"-rrrr-LILlli·CIl·
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·
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-I----r---
ll--q
--
------·-·-·-C--.-L--slrrr-L--·XI^--·
---·-----
--------r
---
UNICLASSIFIED
Security Classification
3ND PPSO 13152
DOCUMENT CONTROL DATA - R&D
(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified)
1. ORIGINATING ACTIVITY (Corporate author)
2a. REPORT SECURITY
Research Laboratory of Electronics
Massachusetts Institute of Technology
Cambridge, Massachusetts
C LASSIFICATION
Unclassified
2b
GROUP
None
3. REPORT TITLE
The Haystack-Millstone Interferometer System
4. DESCRIPTIVE NOTES (Type of report and inclusive dates)
Technical Report
5. AUTHOR(S) (Last name, first name, initial)
Rogers,
Alan E. E.
6. REPORT DATE
7a. TOTAL NO. OF PAGES
Mnrch 15, 1967
9a. ORIGINATOR'S
DA 28-043-AMC-02536(E)
b.
1
60
CONTRACT OR GRANT NO.
8.
7b. NO. OF REFS
4
REPORT NUMBER(S)
Technical Report 457
PROJECT NO.
200-14501-B31F
9
41
NASA Grant
sG- 419
N sGGrant N
NASA
REPORT
9b. OTHER
this report)
N(S) (Any other numbere that may be assigned
10. AVAILABILITY/LIMITATION NOTICES
Distribution of this report is unlimited.
11. SUPPLEMENTARY NOTES
12. SPONSORING MILITARY ACTIVITY
Joint Services Electronics Program
thru USAECOM, Fort Monmouth, N. J.
13. ABSTRACT
The Haystack 120-ft antenna and the Millstone 84-ft antenna have been coupled
together to form a radiometric interferometer. At 18-cm wavelength, which was
chosen for a study of galactic OH emission, the interferometer has a minimum
fringe spacing of 54 seconds of arc.The interferometer synthesizes a beam approximately equivalent to that of a 200.0-ft parabolic antenna and can measure positions
to a small fraction of the fringe spacing. The interferometer uses a digital correlator to analyze the fringe amplitude and phase as a function of frequency. This
enables mapping of spectral features. The design and construction are described,
as well as the theory and method of data reduction. A noise analysis shows that the
threshold level could be reduced by using more complex processing techniques. It
is shown that for radiometric studies many of the capabilities of a very large
antenna can be synthesized, with smaller antennas and complex data-processing
equipment taking the place of mechanical structure.
DD
D
D1
....
.^.____
__
JORM
JAN
6
1473
4
1IA 0101 807 6800
UNCLASSIFIED
Security Classification
.........
..
.
11----------
LX--I I
UIIU
-
-
·- 11
UNCLASSIFIED
· ____
Security Classification
.
.
14.
KEY
WORDS
LINK
ROLE
I
A
WT
LINK
ROLE
B
LINK
WT
ROLE
C
WT
Radiometric interferometer
Haystack
Millstone
Noise analysis
Digital correlator
Spectial line interferometer
aperture synthesis
Radio Astronomy
Servo-controlled transmission line
Microwave interferometer
I
m
_
. pA~-....
_
D , o"v.. 1473
S/N
----
0101-807-6821
I
(BACK)
I
.........
I
d
UNC.T ,ASSIFTFn
Security Classification
A-31
409